Nowadays, patients with mild and moderate upper limb paralysis caused by cerebral apoplexy are uncomfortable with autonomous rehabilitation. In this paper, according to the “rope + toothed belt” generalized rope drive design scheme, we design a utility model for a wearable upper limb rehabilitation robot with a tension mechanism. Owing to study of the human upper extremity anatomy, movement mechanisms, and the ranges of motion, it can determine the range of motion angles of the human arm joints, and design the shoulder joint, elbow joint, and wrist joint separately under the principle of ensuring the minimum driving torque. Then, the kinematics, workspace and dynamics analysis of each structure are performed. Finally, the control system of the rehabilitation robot is designed. The experimental results show that the structure is convenient to wear on the human body, and the robot’s freedom of movement matches well with the freedom of movement of the human body. It can effectively support and traction the front and rear arms of the affected limb, and accurately transmit the applied traction force to the upper limb of the joints. The rationality of the wearable upper limb rehabilitation robot design is verified, which can help patients achieve rehabilitation training and provide an effective rehabilitation equipment for patients with hemiplegia caused by stroke.